Having an advantage isn’t enough

Note: Not at the old Poker1 site. A version of this entry was originally published (2008) in Bluff magazine.

Some stuff is too weird for most people to understand. Time slows down as you move faster. Most of our universe consists of dark matter and dark energy. We can’t see it. And we don’t know what it is. Fine. But there’s also strangeness happening every single day when we gamble — when we play poker.

Think about this: Sometimes betting with an advantage puts you at a disadvantage. Sure, it’s difficult to understand, but you need to grasp it in order to make top-quality decisions in poker and in life. Among skilled gamblers who are emotionally stable and trying hard to make a profit, failure to understand that concept is the single most likely cause of bankroll meltdown. This failing is especially harmful in poker tournaments. So, I guess I should tell you how it works.

Broad decisions

It’s always a mistake to think about whether you’re getting a bargain at the moment or about whether the odds are currently in your favor. You need to base your decisions more broadly than that. You need to think: What’s the best use I can get out of this money? Sometimes using your bankroll most effectively means declining to wager when you have an advantage on one bet, examined in isolation.

Let’s revisit a concept from this column two years ago. I told you that you’re taking the worst of any even-money bet. And if you’ll forgive me for repeating a few short paragraphs, here’s how I explained it:

A major coin flip

… imagine that you were offered a coin-flip bet by a friend. Each of you had a $1,000,000 bankroll, a substantial sum gathered over 20 years of dedicated poker play and representing your entire worldly worth. Your friend, Paul, says, “Let’s flip a coin for $900,000.”

Suppose that, on an impulse, you accept this wager. Since there’s no expertise involved in the coin flip, you correctly reason that the outcome is fifty-fifty and both players, you and Paul, are equally skilled. You might also think that this is what mathematicians would call a “zero-sum game.” That means that every dollar lost is exactly balanced by a dollar won, so there is no net win or loss. But I believe there is a net loss!

In order to see this net loss, you must look beyond the dollars exchanged. You must ask yourself what the effect of the wager will be. If you lose the coin flip you’ll have only $100,000 and Paul will have $1,900,000. Your future will have been brutalized. Paul’s future, though, will have been enhanced nicely, but not overwhelmingly.

Bad for both

Okay. Let’s take this to an even greater extreme to pound in the point. Suppose I offer you 3-to-2 on your entire fortune. We shuffle a deck of cards, you cut, and I turn over the top card. If it’s black, I pay you 1½ times your net worth. If it’s red, you lose everything. Clearly, you have an advantage. My proposed wager is bad for me — but it’s also bad for you. That’s because, while ending up with two-and-a-half times what you started with will make your life considerably more comfortable, going broke overwhelms it. Being broke negatively outweighs the gain by much more than 3-to-2, when weighed in terms of your life’s disruption. You need to think in terms of making your bankroll grow without the threat of instant devastation. And, likely, you’ll find other ways to get a long-term 3-to-2 edge or even greater. Getting there will take longer, but you’ll be much safer.

It’s the same if you’re playing heads-up poker against a weaker player you know you can beat. You might be tempted to double the stakes, but that gives your opponent a better chance of getting lucky, winning big, and perhaps deciding to quit. You might think you’re doubling up with an advantage, but you’re almost certainly going to take this person’s money without the extra risk. Again — a little more time, a little more safety. That’s how you optimize your advantages and build your bankroll.

Avoid calling

Here’s a common way that this concept comes up in proportional-payoff poker tournaments — events where first place gets a percentage of the prize pool, second place a smaller percentage, and so forth. In that normal style of tournament, you need to avoid calling with most speculative hands — especially against weaker opponents you’re likely to get another shot at. In regular ring-game poker, if you’re getting 5-to-1 on a 4-to-1 shot, you should take it. You have an advantage. But in tournaments where you’re a money favorite, you seldom should risk being eliminated or badly damaged with a small overlay. When you have a quality drawing hand after the flop, it’s usually wrong to call a big bet.

So, am I saying you shouldn’t play those hands, even with an overlay? No. I’m not saying you shouldn’t play them. I’m saying you usually shouldn’t call with them. Betting them is a different issue entirely. I’ll frequently bet large with speculative hands that have nearly a 50 percent chance of winning in a showdown. That winning chance is a mixture of the opportunities to make a straight or a flush and the chances of making a pair, two pair, or three of a kind. Okay. But when I make that large bet, I’m hoping to snare the pot right then. That will frequently happen.

Already in the pot

If that primary mission fails, then I still have the best of it, considering that I’m going to win more than half the time and that there were chips already in the pot in addition to my called wager. That provides an overlay as a consolation if my bet fails to snare the pot immediately. Advice: In proportional-payoff tournaments, if you’re a superior player, avoid calling large wagers trying to make straights or flushes — even if you have an overlay and would routinely call if this weren’t a tournament.

Remember, your decision regarding whether and how much to wager shouldn’t be based only on the immediate edge. You need to seek the best bargain you can get for your money. Building a big poker bankroll means learning to be a good shopper. — MC

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Mike Caro

Known as the “Mad Genius of Poker,” Mike Caro is generally regarded as today's foremost authority on poker strategy, psychology, and statistics. He is the founder of Mike Caro University of Poker, Gaming, and Life Strategy (MCU). See full bio → HERE.

@rich – I’ve read Fortune’s Formula. I guess I was trying to say that Kelly is a mathematical description of a similar concept to what Mike is writing about in this article. Namely, don’t bet in such a way as that you’ll do significant harm to yourself (bankroll) going forward.

The consequence of Kelly is that if you always bet using his criteria, you will ultimately win since you’ll never lose enough should you hit a scenario where you end up on the losing side of the odds given incomplete information. Even with Kelly’s criteria there can be massive volatility but one theoretically never go bankrupt. It’s for this reason that many choose to do a half Kelly. I should also add that people obviously cannot calculate Kelly on the spot (i.e., while playing). It’s more a rule of thumb in these cases (like Mike’s article). Using computer software against something like the stock market is precisely where one theoretically could use Kelly in practice. If you’ve read Fortune’s Formula you know what happened in that scenario.

Mike: Thanks for another great suggestion, although I imagine it pains you to comment on proportional payout tournaments.
ph: More on the Kelly criterion – http://www.albionresearch.com/kelly/ Much more math than I can apply at a poker table. That site led me to a book buy; Fortune’s Formula by William Poundstone.
Rich

Interesting perspective. Basically, if the bet you take will cripple you in the future (should you lose) — leaving you broke, not enough to playback and recover your loss, etc. — even though you have an advantage now it should most likely not be taken. Go and find a better gamble.

It reminds of one of the “lessons” from the Kelly Criteria: only bet with half the amount per wager in particular games such at that you can never go broke. (I know that is an inexact representation of Kelly, but it serves it’s purpose here.)